Lesson 8.1--Variation Functions
Solve problems involving direct and joint variation. direct variation
constant of variation
joint variation
In Chapter 2, you studied many types of linear functions. One special
type of linear function is called direct variation.
A direct variation is a relationship between two variables x and y that
can be written in the form
or y = kx, where k ≠ 0.
In this relationship, k is the constant of variation. For the equation
or, y = kx, y varies directly as x.
Example:
Given: y varies directly as x, and y = 27 when x = 6. Write and graph the direct variation function.
1
Example:
Given: y varies directly as x, and y = 6.5 when x = 13. Write and graph the direct variation function.
Example:
The cost of an item in euros e varies directly as the cost of the item in dollars d, and e = 3.85 euros when d = $5.00. Find d when e = 10.00 euros.
A joint variation is a relationship among three variables that can
be written in the form
or y = kxz, where k is the
constant of variation. For the equation
varies jointly as x and z.
or y = kxz, y
2
Example:
The volume V of a cone varies jointly as the area of the base B and the height h, and V = 12π ft3 when B = 9π ft3 and h = 4 ft. Find b when V = 24π ft3 and h = 9 ft.
Example:
The lateral surface area L of a cone varies jointly as the area of the base radius r and the slant height l, and L = 63π m2 when r = 3.5 m and l = 18 m. Find r to the nearest tenth when L = 8π m2 and l = 5 m.
.
HW p. 574 17­23, 39, 40, 49, 52, 53 = 12 problems
3